Edgar borrowed a total of $10,000 from three sources: the bank, his mom, and a close friend. After one year, he paid a total of $624 in simple interest toward the three loans. The bank charged an interest rate of 7% per year, his mom charged 5%, and the friend charged 6%. The amount he borrowed from his mom exceeded the amount he borrowed from his friend by $200. What amount did Edgar borrow from the bank?

Question

10-05-2024
Mathematics

Answered

Edgar borrowed a total of $10,000 from three sources: the bank, his mom, and a close friend. After one year, he paid a total of $624 in simple interest toward the three loans. The bank charged an interest rate of 7% per year, his mom charged 5%, and the friend charged 6%. The amount he borrowed from his mom exceeded the amount he borrowed from his friend by $200. What amount did Edgar borrow from the bank?

Answer :

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unsmartmike unsmartmike · Answer 1 · 2024-05-10T21:49:21-04:00

Answer:

$1,875

Step-by-step explanation:

B as the amount borrowed from the bank.

M as the amount borrowed from his mom.

F as the amount borrowed from his friend.

Given:

1. The total interest paid after one year is $624.

2. The interest rates are 7% for the bank, 5% for his mom, and 6% for his friend.

3. The amount borrowed from his mom exceeds the amount borrowed from his friend by $200.

We can set up the following equations:

1. For the total interest paid:

0.07B + 0.05M + 0.06F = 624

2. For the difference between the amounts borrowed from mom and friend:

M = F + 200

And we know that the total borrowed is $10,000:

B + M + F = 10000

We'll solve this system of equations step by step.

Substitute M=F+200 into the total borrowed equation:

B+(F+200)+F=10000

B+2F+200=10000

B+2F=9800 ...(1)

Now we can substitute this value of M into the equation for the total interest paid:

0.07B + 0.05 (F+200) + 0.06F = 624

0.07B + 0.05F + 10 + 0.06F= 624

0.07B + 0.11F = 614

Now we can use equation (1) to solve for

0.07B + 0.11 (4900−B) = 614

0.07B + 539 − 0.11B = 614

−0.04B + 539 = 614

−0.04B = 75

B = 75/-0.04

B=1875

So, Edgar borrowed $1,875 from the bank.